Real Algebraic and Analytic Geometry
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Submission: 2006, December 23.
We construct a model complete and o-minimal expansion of the field of real numbers such that, for any planar analytic vector field X and any isolated, non-resonant hyperbolic singularity p of X, a transition map for X at p is definable in this structure. This structure also defines all convergent generalized power series with natural support and is polynomially bounded.
Mathematics Subject Classification (1991): 37C27, 37E35, 03C64.
Keywords and Phrases: Dynamical Systems; Logic.
Full text: http://arxiv.org/abs/math.DS/0612745